Answer
$\frac{11}{72}$
Work Step by Step
Define the events
$A_{1}$ = "Heads." $\quad P(A_{1})=0.5$
$A_{2}$ = "Tails." $\quad P(A_{2})=0.5$
$B$ = "Sum of the faces of the dice is $6$"
Compute $P(B|A_{1})$:
If one die is cast, there is one favorable outcome out of $6$.
Thus, $P(B|A_{1})=\displaystyle \frac{1}{6}$.
Compute $P(B|A_{2})$:
If two dice are cast, there are $36$ possible outcomes. The outcomes resulting in a sum of $6$ are
$(1,5),(5,1),(2,4),(4,2)$ and $(3,3)$.
Thus, $P(B|A_{2})=\displaystyle \frac{5}{36}$.
We can now apply the theorem
$$\begin{align*}
P(B)&=\displaystyle \sum_{i=1}^{n}P(B|A_{i})P(A_{i}) & & \\
&= \displaystyle \frac{1}{6}\cdot\frac{1}{2}+ \frac{5}{36}\cdot\frac{1}{2} \\
& =\frac{11}{72} \end{align*}$$
